Seismic data are typically gathered using an array of detectors. In the case of marine data, hydrophones measure pressure fluctuations in the water caused by incoming seismic waves. Geophones measure vector quantities such as displacement, velocity or acceleration. In the case of marine data, a plurality of cables or streamers, which are spaced apart typically by about 100 meters, are towed behind a boat. Each cable has detectors spaced along the cable at intervals. In the case of land data, a geophone array is laid out on the ground with the geophones in an approximate grid formation. The detector array detects seismic signals from reverberations of a signal from a seismic source, such as an airgun for marine data. In Ocean Bottom (OBC or OBS) acquisition, a detector array is fixed on the sea bed. The source may be an airgun mounted on a boat.
As illustrated in FIG. 1a, the direction in which the source moves, which in a marine environment is the direction in which the boat sails, is referred to as the inline direction. The perpendicular direction is the crossline direction. Lines of receivers, which are streamers in a towed streamer marine acquisition, are spaced apart in the crossline direction.
In a towed streamer system, ideally the streamers would be parallel, but in reality due to currents etc. there will be drift of the streamers, particularly towards the free ends. Some acquisition systems include streamer steering to maintain the streamers as close to being parallel as possible. Each streamer includes a plurality of receivers which are typically spaced equally along the length of the streamer. A source is positioned behind the boat, typically between the boat and the fixed end of the streamers. The source, typically an air gun, fires a seismic signal at intervals as the boat sails in the inline direction. Shots may be fired, for instance, every 25 meters. The streamer spacing in the crossline direction is typically of the order of 100 meters. The receiver spacing along the streamers may also be the order of approximately 25 meters and the streamers may be several kilometers long, with 6-10 km being a typical range. The receivers record seismic energy which is reflected from the ocean bottom and various reflectors or boundaries between geological layers in the earth.
It is well known that an interface will reflect sound waves at a magnitude that is dependent on the relative velocities of the sound waves in the medium on either side of the interface. Therefore, because water and air have a large difference in seismic velocity, the air/water interface at the water surface has a very high reflection coefficient. Therefore, one problem in processing marine seismic data (both with towed streamer acquisition and OBC acquisition) is free surface multiples which result from seismic energy which is reflected from the free surface, possibly having already been reflected from the earth. Because of the high reflection coefficient, these free surface multiples appear as high magnitude events on a seismic profile thus obscuring data from real sub-surface events.
A number of data processing algorithms exist for the attenuation of surface related multiples. Algorithms can operate on 3D data, i.e. data having source and receiver positions covering a surface grid, or on 2D data where the source and receiver positions are located on a single line. Methods applied to 3-D data generally have the disadvantage of being computationally intensive whereas methods applied to 2D data may be less accurate.
Surface related multiple elimination (SRME) algorithms can be divided into iterative and non-iterative SRME methods.
In iterative SRME algorithms, approximations in the modeling are handled approximately by processing a model of free-surface multiples, computed at each iteration of SRME, by applications of matching filters. In addition, the amplitude correction that should be applied before processing 3D with a 2D algorithm is in general applied in a form valid for constant velocity media only.
Matson and Corrigan (“2.5D Method for Attenuating Free-Surface Multiples Based on Inverse Scattering Series”, Proceedings of the Annual Off-Shore Technology conference 1, pages 309 to 318, 2000) discloses 2D, 3D and 2.5D iterative multiple attenuation methods for towed streamer data. In the 2.5D approach, a 3D algorithm is specialised to the case where the earth can be assumed invariant (or slowly variant) in one direction, on a scale relevant for a seismic survey.
Examples of non-iterative algorithms are disclosed in Dragoset and Jericevic (U.S. Pat. No. 5,587,965) and Amundsen et al., (“Multidimensional Signature Deconvolution and Free-Surface Multiple Elimination of Marine Multicomponent Ocean-Bottom Seismic Data”, Geophysics Vol. 66, No. 5, pages 1594 to 1604, 2001). Amundsen et al. disclose a method using ocean-bottom cable data wherein the input data are separated into up-going and down-going wave fields and a multiple dimensional deconvolution operator is derived from the down-going wave field. This is referred to as the MAUDD (Multiple Attenuation by Up/Down Deconvolution) algorithm. In the MAUDD approach, the input data is separated into upgoing and downgoing wavefields, and a multi-dimensional deconvolution operator is derived from the downgoing wavefield. The Amundsen method is often applied to wide-azimuth sea-bed data assuming a 1D earth (with properties varying with depth only); applications of the 2D algorithm to sea-bed data have also been reported.
Although iterative SRME methods are currently the most popular ones, other approaches have been suggested that try to improve on some aspects of SRME. For instance, the model produced by iterative SRME doesn't correctly predict the amplitudes of all orders of multiples (especially at initial iterations, when the modeling operator(s) is built from data rather than from primaries). Non-iterative SRME methods, such as the method published by Dragoset and Jericevic offer an alternative approach, which has been restricted to applying a 2D algorithm to 3D data.